W. Falck, O.N. Bjørnstad and N.C. Stenseth: Bootstrap estimated uncertainty of the dominant Lyapunov exponent for Holarctic microtine rodents

Proceedings of the Royal Society of London B (1995) 261: 159-165


The dominant Lyapunov exponent, as estimated from time series through the Jacobian-based method, is often used for indicating whether the underlying dynamic system is chaotic or not. The Jacobian-based method together with Response Surface Methodology (RSM) has recently been suggested as a method for detecting chaotic dynamics in time series. Besides pointing out that this may not be an appropriate method, we report on estimates of the uncertainty in the estimates of the dominant Lyapunov exponent. For this purpose, we have used time series data on Holarctic microtines. On the basis of our analyses, we are unable to find any convincing evidence for chaotic dynamics in Northern microtine populations (north of 60° N) recently suggested in the ecological literature. It seems, however, that the dynamic properties of the Northern and Southern populations are different. These patterns are supported by testing for non-linearity.

Key words: bootstrap, chaos, Lyapunov exponent, population dynamics, response surface, modeling, microtine rodents, uncertainty